Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#16810462 | C2 | semidirect |
| 3. #20276806 | C2 | semidirect |
| 4. #20272894 | C2 | semidirect |
| 5. C53×C22⋊C32 | C2 | semidirect |
| 7. C2×Dic424 | C22 | semidirect |
| 13. #16810449 | C22 | semidirect |
| 16. C2×C32×C53 | C22 | semidirect |
| 78. C22×C53 | SD64 | semidirect |
| 93. C22⋊C32 | D53 | semidirect |
| 107. C2×C32 | C2×D53 | semidirect |
| 110. C53 | #13664 | semidirect |
| 175. C22 | #16810462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C2×#16810462 | 2 |
| #20276806 | 2 |
| #20272894 | 2 |
| C53×C22⋊C32 | 2 |
| #13664 | 53 |